MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Subhra Dutta Grade:
        

how to determine the centre of mass of a solid hemisphere

7 years ago

Answers : (2)

Pratham Ashish
17 Points
										

 


 consider the  hemisphere  shown below the solution , let the mass of it be M & radius be R


then , mass density , ρ = M / {2/3 ¶ R ^3}


 from the symmetry of object we can say the C.M. will lie on the vertical axis shown in the figure


take a disk of dl length at the l distance from O, its C.M. will be at its centre means at the l distance from O


its mass  dm =  ρ  dv


                    = ρ  ¶ r^2 dl


                    =   ρ  ¶  ( R^2 - l^2 ) dl


 


C.M. of mass of hemisphere =


                                          = 1/M  ∫ dm l


                                          = 1/M ∫ ρ  ¶  ( R^2 - l^2 ) dl  *l


                                           =  ρ  ¶ / M ∫ l ( R^2 - l^2 ) dl 


                                           =  ρ  ¶ / M [R^2 * l^2 /2   -  l^4 /4  ]0 R


                                           = ρ  ¶ / M ( R^4) /4


                                            = ρ  ¶ (R^4) / { ρ *2/3 *4 *  ¶ R ^3}


                                            = 3 R/ 8       from O at the axis of symmetry


 


 


 


 


 


4567-704_4788_7.bmp

7 years ago
satyapreet singh
18 Points
										

the solid hemisphere is a symmtrical body about the coordinate axes, i mean is symmtrical about X , Y axes. therefore its centre of mass lies on its centre.

7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete Physics Course - Class 12
  • OFFERED PRICE: R 2,600
  • View Details
Get extra R 520 off
USE CODE: CART20
  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details
Get extra R 560 off
USE CODE: CART20

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details